It has long been known that techniques of spatial multiplexing can be used to improve the spectral efficiency of wireless networks. (Spectral efficiency describes the transmitted data rate per unit of frequency, typically in bits per second per Hz.) In typical examples of spatial multiplexing, a multiple array of transmit antennas sends a superposition of messages to a multiple array of receive antennas. The channel state information (CSI), i.e., the channel coefficients between the respective transmit-receive antenna pairs, is assumed known. Provided that there is low correlation among the respective channel coefficients, the CSI can be used by the transmitter, or the receiver, or both, to define a quasi-independent channel for each of the transmitted messages. As a consequence, the individual messages are recoverable at the receiving antenna array.
More recently, experts have proposed extensions of the spatial multiplexing technique, in which a multiplicity of mobile or stationary user terminals (referred to herein as “terminals”) are served simultaneously in the same time-frequency slots by an even larger number of base station antennas or the like, which we refer to herein as “service antennas”, or simply as “antennas”. Particularly when the number of service antennas is much greater than the number of terminals, such networks may be referred to as “Large-Scale Antenna Systems” (LSAS).
Theoretical studies predict that the performance of LSAS networks scales favorably with increasing numbers of service antennas. In particular, there are gains not only in the spectral efficiency, but also in the energy efficiency. (The energy efficiency describes the ratio of total data throughput to total transmitted power, and is measured, e.g., in bits per Joule.)
One such study is T. L. Marzetta, “Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas,” IEEE Trans. on Wireless Communications 9 (November 2010) 3590-3600, hereinafter referred to as “Marzetta 2010”.
In some approaches, the base stations may obtain CSI through a procedure that relies on time-division duplex (TDD) reciprocity. That is, terminals send pilot sequences on the reverse link, from which the base stations can estimate the CSI. The base stations can then use the CSI for beam-forming. This approach works well when each terminal can be assigned one of a set of mutually orthogonal pilot sequences.
Generally, it is considered advantageous for the terminals to synchronously transmit all pilot sequences on a given frequency, and possibly even on all frequencies, making use of the mutual orthogonality of the pilot sequences.
The number of available orthogonal pilot sequences, however, is relatively small, and can be no more than the ratio of the coherence time (an interval during which prevailing channel conditions between a base station and a terminal are assumed to be static) to the delay spread (the difference between the time of arrival of the earliest significant multipath component and the time of arrival of the latest multipath component). Terminals within a single cell can use orthogonal pilot sequences, but terminals from the neighboring cells will typically be required to reuse at least some of the same pilot sequences. This reuse of pilot sequences in different cells creates the problem of pilot contamination. The pilot contamination causes a base station to beam-form its message-bearing signals not only to the terminals located in the same cell, but also to terminals located in the neighboring cells. This phenomenon is known as directed interference. The directed interference does not vanish as the number of base station antennas increases. In fact, the directed inter-cell interference—along with the desired signals—grows in proportion to the number of base station antennas.
As shown in Marzetta 2010, for example, as the number of base station antennas grows in an LSAS network, inter-cell interference arising from pilot contamination will eventually emerge as the dominant source of interference.
One approach for suppressing inter-cell interference and thus achieving even greater signal to interference and noise ratios (SINRs, or singularly, SINR) has been to subdivide an LSAS network into clusters. Cluster-based schemes exist for mitigating directed inter-cell interference for cells within each respective cluster.
However, one disadvantage of the cluster-based approach to suppressing inter-cell interference is the likelihood of inter-cluster interference for terminals located along a cluster perimeter. The number of terminals located along a cluster perimeter is typically large, particularly in the case of a large network in which there are many clusters. Thus, a significant portion of terminals may be affected by inter-cluster interference and served with relatively low data transmission rates. Further, increasing the size of clusters to lower the amount of terminals located along a cluster perimeter will also increase the size of cluster perimeters, making it more likely that a larger number of terminals will be located relatively near to a cluster perimeter at a given time. In addition, larger clusters may require cooperation between relatively larger numbers of base stations, which also can increase complexity.